Cyclicity of degenerate graphic DF2a of Dumortier-Roussarie-Rousseau program

Abstract

In this paper we finish the study of the cyclicity ( i.e. the maximum number of limit cycles) of the degenerate graphic DF2a of [6] which is initiated in [5]. More precisely, we prove that the graphic DF2a has a finite cyclicity. The goal of the program [6] is to solve the finiteness part of Hilbert’s 16th problem for quadratic polynomial systems. We use techniques from geometric singular perturbation theory, including the family blow-up.